I'm assuming that you mean by "I got a new computer" you really mean "I got a computer that is used, but is new to me!" as that model has not been made for several years. Regardless, the video that is 'built in' to that system is not sufficient for any kind of performance (or reliability) in aces high as it uses the Intel® Graphics Media Accelerator 3000 chip. It has been proven time and time again that this built in video chip has issues exactly like what you describe.
It actually does have a PCI-e slot, but only at 1X speed and while a PCI-e video card running at 1X speed is probably still an improvement over the onboard Intel graphics, you're still going to be limited by the 300watt power supply.
Even though the processor sounds good on paper (dual core 3.4 GHz processor!) it really can't hold its own if compared to modern processors even at lower speeds!
I have to assume that the computer was purchased as a "recertified" or "off-lease" deal... sounds about right for what you can find in the $100-125 range but the problem is you're going to be spending at least that much more to upgrade it well enough to handle any games, and you're still going to have an inferior system... by far. If you can't afford it then you can't afford it, but for about $500 or so you can build a system decent enough to run Aces High at 'almost' full boat settings that is going to last you at least for awhile.
I'm sure there are PCI-e video cards out there that will be fine with a puny power supply like that (and perform much better than the on-board video you have) for probably $40-50 or so, but the next Aces High graphics update is going to put you in the same exact pickle again.
Good luck!
